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Number of numbers of the form x^3+y^2+x*y less than or equal to n (x,y >=0).
0

%I #5 Mar 30 2012 18:39:04

%S 1,3,3,4,5,5,5,6,7,8,8,9,9,10,10,10,12,12,12,12,12,13,13,14,14,15,15,

%T 16,16,16,16,18,19,19,19,19,20,21,21,21,21,21,21,23,23,24,24,24,24,25,

%U 25,25,25,25,25,26,27,28,28,28,28,28,28,28,30,30,30,31,31,32,32,33,33

%N Number of numbers of the form x^3+y^2+x*y less than or equal to n (x,y >=0).

%F Using Ikehara's theorem one can show that a(n) is asymptotic to C*n^(5/6) where C is a positive constant >0.7

%e 0^3 + 0^2 + 0*0, 0^3 + 1^2 + 0*1, 1^3 + 0^2 + 1*0 are 3 numbers <= 1 hence a(1) = 3.

%o (PARI) a(n)=sum(i=0,n,sum(j=0,n,if((sign(i^3+j^2+i*j-n)+1)*sign(i^3+j^2+i*j-n),0,1)))

%K nonn

%O 0,2

%A _Benoit Cloitre_, Aug 14 2002